which of the following statements best describes a trigonometric function having undergone a phase shift? select all that apply.

the graph of y = sin x is translated three units down.
the graph of y = csc x is translated three units to the right.
the graph of y = cos x is translated three units up.
the graph of y = sec x is translated three units to the left.
the graph of y = cot x is reflected over the horizontal axis.
the graph of y = tan x is reflected over the vertical axis.

Options B and D

Step-by-step explanation:

Phrase shift of a trignometric function is the horizontal shift of the function towards right or left.

Vertical shift is shift up or down.

The graph of y = sin x is translated three units down.

-- This is vertical shift and not phase shift.

The graph of y = csc x is translated three units to the right

-- This is a phase shift as y = csc (x+3)

The graph of y = cos x is translated three units up.  -- No, vertical shift.

The graph of y = sec x is translated three units to the left. -- Yes, phase shift

The graph of y = cot x is reflected over the horizontal axis. -- No, reflection

The graph of y = tan x is reflected over the vertical axis.-- No, reflection

Only options B D are phase shifts.

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step-by-step explanation: